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First-Principle Measurements: An Important Concept

Updated: Mar 6


 

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What is a direct first-principle measurement? Why is it important? What does it have to do with uncertainty? What is “compounding uncertainty” in indirect measurements?

Rather than spending time on definitions, let us start by an example:



Example: Direct and Indirect Measurement of a Cube Volume


Consider measuring each side of a cube with a ruler that has a 10% uncertainty. In this scenario, the compounding nature of uncertainties becomes apparent. The subsequent calculation of the cube's volume, due to this compounding effect, results in a 30% uncertainty. This example vividly illustrates how uncertainties, when combined in mathematical operations, can magnify the overall level of uncertainty in the result.



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Example of measurement



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Measurement example

In this case, our objective was measurement of the volume, and we measured it as directly as possible. This means we measured the property we were interested in, without relying on other properties or calculations. When we measure a property directly, when it's based on a fundamental physical principle, we are making a “first-principle measurement”.


Application in Gas Measurement: Navigating the Complexities of Moisture Analysis


Generally, direct measurements often minimize uncertainties, making it crucial to choose methods carefully. Now, let’s Extend this concept to natural gas, focusing on moisture analysis. Contrasting direct dew point measurement with indirect moisture content measurement using an aluminum oxide sensor highlights the tangible benefits of first-principle measurements.


Direct Measurement of Dew Point


The dew point of gas is solely influenced by its moisture level and pressure, with a slight impact from its composition. Measuring the dew point involves cooling a component, identifying condensation, and recording the temperature when condensation occurs. The critical factor in this process is temperature. If you have a dependable temperature sensor and are certain the condensation is water, your measurement's precision is primarily determined by the temperature sensor's uncertainty, which is generally quite low.





Indirect Measurement of Dew Point (Using Aluminum Oxide Sensor)

Now, let's look at how we measure moisture using an aluminum oxide sensor. First, moisture goes through a barrier that's supposed to only let water molecules pass, but it's not perfect, especially in natural gas. The water molecules that make it through cause a change in a capacitor's ability to store energy, and we measure this change using electronic circuits. We then use calibration tables to figure out how much moisture is in the gas. But, to make this method work well, we have to assume a few things:


  1. The permeation rate of water molecules through the barrier stays the same.

  2. No other molecules interfere with the capacitor's ability to store energy.

  3. The change in the capacitor's ability to store energy per water molecule doesn't change over time.

  4. The electronic circuits measuring the change in the capacitor are very accurate with low uncertainty.

  5. The initial calibrations of the sensor at the factory have low uncertainty and are still valid; i.e. the sensor has not drifted.


Unfortunately, these assumptions aren't always valid, especially when dealing with moisture in natural gas. Each assumption and measurement come with their own uncertainties, like how fast moisture moves through the barrier and changes in the capacitor. All these uncertainties add up, making the overall uncertainty bigger than we first thought.


Critical Considerations in Gas Measurements

In the complex realm of natural gas analysis, opting for direct measurements is essential. This requires careful consideration of the core property, choosing the most direct and accurate measurement methods, and understanding the associated uncertainties. Prudent decision-making is crucial for reliable gas analysis.

Comparing moisture dew point measurements to those using an aluminum oxide sensor illustrates the effectiveness of first-principle measurement. Similar principles apply to other methods like Tunable Diode Lasers (TDL) or Quartz Crystal Monitors (QCM), which we'll explore in detail in future blogs.


EPILOGUE

It's crucial to note that many manufacturers of moisture measurement instruments, including aluminum oxide, QCM, and TDL, misleadingly label their devices as dew point sensors. They are not.

Dew point can only be accurately measured using the chilled-mirror principle. These other instruments measure moisture content (with all its compounded uncertainty) and then calculate a dew point. Describing these instruments as Dew Point analyzers, Dew Meters, or any similar term involving "Dew" is misleading.

So, when you're in the market for a dew point analyzer, make sure to ask the vendor whether their instrument genuinely measures dew point or if it's being labeled for marketing purposes.



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